This article is one of a series that describes how to calculate sample sizes for different experimental conditions and distribution types. Here, a step by step process of the sample size calculation method is outlined. It is intended to be used before any experiment is started. A free sample size calculator is available, for various power values.
Sample Size Calculation: Define The Data Type and Distribution
There are four main types of data distribution for which sample sizes are usually estimated. These are means, standard deviations, proportions, and rates. There may be several choices of variable for each experiment, but in general, it is better to choose variables that follow a Gaussian ("Bell-curved") distribution. The reason is that smaller sample sizes are usually needed. Similarly, smaller sample sizes are usually needed for continuous variables (e.g. measured values) than for discrete variables (e.g. Pass / Fail).
Sample Size Calculation: Decide To Use a One-Sample or Two-Sample Test
This distinction is easier to understand when considering that a sample may differ from the population from which it comes. In other words, samples contain a degree of "error", and are estimates. Where there is a well-established and accepted baseline, a one-sample test may be used. The question that the experiment is designed to answer is of the form:
"Does a new machine produce parts with a mean of 1.25 inches?", or
"Does new drug A give a median survival time of 5 years?"
The equivalent two-sample examples are:
"Does a new machine produce parts with the same mean as another new machine?", or
"Does new drug A give a median survival time that is comparable to another new drug B?"
Sample Size Calculation: Decide To Use a One-Sided or Two-Sided Test
This question is designed to find out if a change (e.g. new drug, new machine, process change, group of people etc.) is different to the "old" situation, or is it better than it. The Null Hypothesis will have defined this already. As an example, a new drug "B" is to be tested. The one-sided null hypothesis would be:
"Drug B is not better than the old drug A", and the two-sided null hypothesis would be
"Drug B is not better than and not worse than old drug A"
In the one-sided test the experimenter only cares if drug B is better than drug A. This may be because it costs the same, and he is only interested if it gives a medical benefit. In the two-sided test, the experimenter is trying to show that the two drugs are equivalent, possibly because drug B costs much less.
Sample Size Calculation: Choose Values For Confidence, Power and Effective Difference
At this stage, the experimenter chooses the values for Confidence and Power. These vary from industry to industry, but tend to be constant throughout individual industries. For many common process industry experiments, confidence level is set to 95% or 0.95, and power is set to 90% or 0.9
The effective difference, or critical difference, is the amount of change or difference that is considered worthwhile. It is often expressed in terms of the ratio of actual difference( e.g. in years etc) divided by the standard deviation.
In general, the more important and costly the experiment will be, the more care must be taken that all relevant sampling and experimental protocols are followed.
Sample Size Calculation: Use Relevant Equation To Do Sample Size Calculation
When the sample size selection method shown here has been followed, the equation that pertains to the circumstances for each variable may be used. Many online statistics sites provide sample size calculators for free.
The number returned by the sample size calculation is usually not an integer. For many experiments, this is not a problem, and a value for sample size of 48.1 may be rounded down to 48. Care must be taken, however, in experiments that could have implications legally: where protocol requires a statistical confidence of 95%, then 94.9% may not be good enough.
Sample Size Calculation Summary
This step by step guide to sample size calculation covers the main distribution types, and should be read together with an article that defines the terms used. The actual formulae used is described in the articles Sample Size Formula for Means and Sample Size Formula for Proportions.
A free sample size calculator is also available.
Sample Size Method References
Julious, S.A., (2009), Sample Sizes for Clinical Trials. Boca Raton: CRC Press.
Martin Bell - Martin holds a B.Sc. degree in chemical engineering, and an M.Sc. degree in electronics and computing. He has spent more than 25 years ...
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